From experience in two European countries, this is not always the case. I have both a Visa and MC cards which can be used in contactless mode for transactions of any size, up to the card limit. For low amounts (<40EUR) the PIN is not requested. For larger transactions I have to enter the PIN, but I don't need the chip.

In the UK, Contactless is PIN free, hence the low floor limit. Anything over that amount (£30 typically) requires Chip+PIN, and remote authentication.

Just from my personal experiance in Switzerland I think this is mostly the case, but not always. I have a contactless Visa with a rather low limit that I use for small day to day purchases. I only use it contactless and most of the time I can go over the monthly limit if I only use it contactless. Sometimes if I do this it will still be declined by a shop due to «insufficient funds», so some contactless terminals must be calling home. At this point the Card stops working at any terminal, even the contactless kind. I have to wait for the next month and use it the Chip and Pin way once to make it work again.